On June 20, 2016, the Buffalo Sabres acquired Vesey's rights from the Predators in exchange for a third-round pick in the 2016 NHL Entry Draft. The deal was made in order to give the Sabres an extra few weeks of exclusive negotiating rights with Vesey before he became a free agent. Despite this, Vesey's agent informed ESPN that he had still intended to become a free agent. While discussions with the Sabres continued, a deal was not struck and in accordance with the NHL CBA, Vesey became an unrestricted free agent on August 16.
On August 20, 2016, Vesey signed with the New York Rangers. After attending the training camp, Vesey received the Lars-Erik Sjöberg Award, which is given to the best Rangers' rookie in the camp. On October 17, 2016, Vesey scored his first NHL goal in a 7–4 win over the San Jose Sharks.